A Cool Algebra Problem

Algebra Level 3

Originally, the ratio of yellow to purple color pencils is 7:2. I lose one purple color pencil every day and three yellow pencils every day. One time, I lose three yellow pencils and lose my last purple color pencil. Surprisingly, I am left with 15 yellow colored pencils. How many pencils were there together originally?

The answer is 135.

1 solution

Noel Lo
Jun 9, 2015

If I have $x$ pencils at first, $\frac{7x}{7+2} = \frac{7x}{9}$ of them are yellow while $\frac{2x}{7+2} = \frac{2x}{9}$ of them are purple. After a certain number of days, I lost $\frac{7x}{9} - 15$ yellow pencils and $\frac{2x}{9}$ . I would also have lost three times as many yellow pencils as purple pencils so:

$\frac{7x}{9} - 15 = 3(\frac{2x}{9})$ .

$\frac{7x}{9} -15 = \frac{6x}{9}$

$\frac{x}{9} =15$

$x=\boxed{135}$ .

A Cool Algebra Problem

The answer is 135.

1 solution

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